We are asked to calculate the volume of a cylinder. The diameter of the circular base is $8$ cm, and the height (or length) of the cylinder is $13$ cm. We need to express the volume in two ways: a) in terms of $\pi$, and b) as a decimal to 2 decimal places.

1. Problem Description

We are asked to calculate the volume of a cylinder. The diameter of the circular base is $8$ cm, and the height (or length) of the cylinder is $13$ cm. We need to express the volume in two ways: a) in terms of $\pi$, and b) as a decimal to 2 decimal places.

2. Solution Steps

First, we need to find the radius of the circular base. The radius is half the diameter:

$r = \frac{d}{2}$

$r = \frac{8}{2} = 4$ cm

The formula for the volume of a cylinder is given by:

$V = \pi r^2 h$

where $r$ is the radius and $h$ is the height (or length).

a) To express the volume in terms of $\pi$, we substitute the values of $r$ and $h$ into the formula:

$V = \pi (4^2)(13)$

$V = \pi (16)(13)$

$V = 208\pi$ cm$^3$

b) To find the volume to 2 decimal places, we multiply $208$ by $\pi \approx 3.14159265359$:

$V = 208\pi \approx 208 \times 3.14159265359$

$V \approx 653.45127124$ cm$^3$

Rounding to 2 decimal places, we get:

$V \approx 653.45$ cm$^3$

3. Final Answer

a) The volume of the cylinder in terms of $\pi$ is $208\pi$ cm$^3$.

b) The volume of the cylinder to 2 decimal places is $653.45$ cm$^3$.